Could the real author of the Shakespearean plays be a woman?

Today I read Yahoo news about Shakespeare, and "they" say they don't think he wrote his plays (because he was from a poor illiterate family .... I guess that if a person was really driven to something they wouldn't learn to write, right? Look at Ben Franklin, or even more Abraham Lincoln ... ). Any way I noticed that the persons they named as possible authors where all men ... But why not women? If I was in that time, when women could not even be actors, and I wanted to write plays, wouldn't I find myself some poor young man to be my representative ...?